Boundary condition | Equation | Description | Equation parameters |
---|---|---|---|
Governing equation | \(\rho {C}_p\frac{\partial T}{\partial t}=K{\nabla}^2T+Q\) | The partial differential eq. of heat conduction through the material | ρ: the specimen’s density (kg cm−3) Cp: the specific heat (J kg−1 K−1) k: The thermal conductivity (Wm−1K−1) Q: represents a distributed heat generation term T: represents the temperature field as a function of time and space (K) |
Conduction heat flux | \(hf=\frac{P}{\pi {r}_b^2}\ {e}^{\frac{-2{r}^2}{r_b^2}}\) | The heat flux occurs on the sample’s top surface | hf: laser heat flux (Wm−2) P: laser power (W) rb: radius of the laser spot at the workpiece’s surface (μm) r:the radial distances from the center of the laser beam point |
Convection heat flux | Qc = Ashc(T − Tamb) | The heat flux occurs at the sample’s boundary | Qc: convective heat flux (W/m−2) hc: coefficient of convective heat transfer (W/m−2 K−1) T: specimen temperature (K) Tamb: ambient temperature (K) |
Radiation heat flux | \({Q}_r={A}_s\varepsilon \sigma \left({T}^4-{T}_{\textrm{amb}}^4\right)\) | ɛ: the material emissivity 𝛔: Stefan–Boltzmann constant (Wm−2 K4) |